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Arithmetic Geometry December 11, 2000 - December 15, 2000
Registration Deadline: December 15, 2000 over 23 years ago
To apply for Funding you must register by: September 11, 2000 almost 24 years ago
Parent Program:
Organizers Noam Elkies, William McCallum, Jean-François Mestre, Bjorn Poonen (chair) and René Schoof

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The workshop will focus on the development of explicit and computational methods in arithmetic geometry, as well as the complexity analysis of existing algorithms. Topics include (but are not necessarily limited to) computational aspects of the following:   determination of rational points on curves and higher dimensional varieties Mordell-Weil groups of elliptic curves and other abelian varieties Selmer and Shafarevich-Tate groups isogenies, endomorphism rings, and torsion subgroups of abelian varieties minimal proper regular models of curves Neron models and conductors of Jacobians equations for modular curves and Shimura curves function field analogues of all the above zeta functions of curves and other varieties over finite fields.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Dec 11, 2000
09:30 AM - 11:00 AM
  Odds and ends on curves of low genus
Armand Brumer (Fordham University)
11:00 AM - 02:00 PM
  Chabauty and covers for curves with an automorphism
Joseph Wetherell
02:00 PM - 03:00 PM
  Uniform Chabauty bounds for twists
Michael Stoll (Universität Bayreuth)
03:00 PM - 04:00 PM
  Diophantine undecidability of function fields of positive characteristic finitely generated over fields algebraic over a finite field
Alexandra Shlapentokh (East Carolina University)
Dec 12, 2000
09:30 AM - 11:00 AM
  Wick's theorem and the calculation of genus one Jacobians
jorgen Anderson
11:00 AM - 02:00 PM
  Reduction of binary forms
John Cremona (University of Warwick)
02:00 PM - 03:00 PM
  Descent calculations for the elliptic curves of conductor 11
Tom Fisher
03:00 PM - 04:00 PM
  The period-index problem
Catherine O'Neil
04:00 PM - 04:25 PM
  Second 2-descents for y2=x3-d2x
Franz Lemmermeyer
04:25 PM - 04:50 PM
  Explicit Weierstrass Preparation Theorem in several variables and rational points on the hyperelliptic curve y2=x9 - 6x8 + 31x7 - 81x6 + 177x5 - 176x4 - 9x3 + 107x2 + 19x + 1
Sylvain Duquesne
04:50 PM - 05:50 PM
  The calculation of periods on HpXH and Heegner points attached to real quadratic fields: a progress report
Henri Darmon (McGill University)
Dec 13, 2000
09:30 AM - 11:00 AM
  Algorithms for computing zeta functions of elliptic curves over finite fields and related topics.
Takakazu Satoh
11:00 AM - 02:00 PM
  Picard-Fuchs equations and computing zeta functions p-adically
Fernando Rodriguez-Villegas
02:00 PM - 03:00 PM
  On the computation of the divisor class group of global function fields
Florian Hess
03:00 PM - 04:00 PM
  On splitting rational places in algebraic extensions of function fields over finite fields
Vinay Deolalikar
04:00 PM - 04:25 PM
  Explicit covering techniques
Nils Bruin
04:25 PM - 04:50 PM
  Algebraic curves of genus at least 2 with many rational points
Leopoldo Kulesz
04:50 PM - 05:50 PM
  Curves of genus two covering elliptic curves
Tanush Shaska (Oakland University; University of California, Irvine; University of Florida; Research Institute of Science and Technology)
Dec 14, 2000
09:30 AM - 11:00 AM
  Visibility of Shafarevich-Tate groups of abelian varieties
William Stein (University of Washington)
11:00 AM - 02:00 PM
  On computing coefficients of eigenforms
Bas Edixhoven (Universiteit Leiden)
02:00 PM - 02:25 PM
  Computation of periods of higher weight modular forms
Helena Verrill (Louisiana State University)
02:25 PM - 02:50 PM
  Shimura curve invariants
David Kohel (Université d'Aix-Marseille (AMU))
02:50 PM - 03:50 PM
  Q-curves over quadratic fields and Jacobian surfaces of GL2-type
Ki-ichiro Hashimoto
03:50 PM - 04:15 PM
  Ljunggren's equation and modular Q-curves
Jordan Ellenberg (University of Wisconsin-Madison)
04:15 PM - 04:40 PM
  Manin ideals for Q-curves
Joan-Carles Lario
04:40 PM - 05:40 PM
  Modular curves of genus 2
Enrique Gonzalez Jimenez
Dec 15, 2000
09:30 AM - 11:00 AM
  Rational points of the group of components of a Néron model.
Qing Liu
11:00 AM - 02:00 PM
  Special fibers of Néron models
Dino Lorenzini
02:00 PM - 02:25 PM
  A Nagao-type formula for elliptic threefolds
Rania Wazir
02:25 PM - 02:50 PM
  Uniformization of Néron models of semistable Jacobians
Fabrizio Andreatta
02:50 PM - 03:30 PM
  Images of three-dimensional Galois representations
Luis Dieulefait (University of Barcelona)
03:30 PM - 03:55 PM
  On the group of automorphisms of Shimura curves and applications
Victor Rotger
03:55 PM - 04:20 PM
  Thue equations and the method of Chabauty-Coleman
Tom Tucker
04:20 PM - 05:20 PM
  From K3 lattices to explicit K3 moduli
Charles Doran (University of Alberta)